IEC 63185:2025

IEC 63185 ®
Edition 2.0 2025-03
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Measurement of the complex permittivity for low-loss dielectric substrates
balanced-type circular disk resonator method

Méthode du résonateur symétrique à disque circulaire pour mesurer la
permittivité complexe des substrats diélectriques à faible perte

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IEC 63185 ®
Edition 2.0 2025-03
INTERNATIONAL
STANDARD
NORME
INTERNATIONALE
Measurement of the complex permittivity for low-loss dielectric substrates

balanced-type circular disk resonator method

Méthode du résonateur symétrique à disque circulaire pour mesurer la

permittivité complexe des substrats diélectriques à faible perte

INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
COMMISSION
ELECTROTECHNIQUE
INTERNATIONALE
ICS 33.120.30  ISBN 978-2-8327-0311-3

– 2 – IEC 63185:2025 © IEC 2025
CONTENTS
FOREWORD . 3
1 Scope . 5
2 Normative references . 5
3 Terms and definitions . 5
4 Measurement parameters . 5
5 Theory and calculation equations . 6
6 Measurement system . 9
7 Measurement procedure . 10
7.1 General . 10
7.2 Preparation of measurement apparatus. 10
7.3 Adjustment of measurement conditions . 10
7.4 Calibration of a vector network analyzer . 10
7.5 Measurement of complex permittivity of test sample . 10
7.6 Periodic checkup of metal in resonator. 11
Annex A (informative) Example of measurement results and associated uncertainties
for complex permittivity . 12
Bibliography . 14

Figure 1 – Structure of a circular disk resonator . 7
Figure 2 – Relation between resonant frequency and relative permittivity. 8
Figure 3 – Schematic diagram of a vector network analyzer measurement system . 9
Figure 4 – Frequency response of S of balanced-type circular disk resonator . 10
Table A.1 – Parameters of the resonator and the sheet sample . 12
Table A.2 – The resonant frequencies and unloaded Q-factors . 12
Table A.3 – Measurement results of complex permittivity . 13

INTERNATIONAL ELECTROTECHNICAL COMMISSION
____________
MEASUREMENT OF THE COMPLEX PERMITTIVITY
FOR LOW-LOSS DIELECTRIC SUBSTRATES
BALANCED-TYPE CIRCULAR DISK RESONATOR METHOD

FOREWORD
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all national electrotechnical committees (IEC National Committees). The object of IEC is to promote international
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8) Attention is drawn to the Normative references cited in this publication. Use of the referenced publications is
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IEC 63185 has been prepared by subcommittee 46F: RF and microwave passive components,
of IEC technical committee 46: Cables, wires, waveguides, RF connectors, RF and microwave
passive components and accessories. It is an International Standard.
This second edition cancels and replaces the first edition published in 2020. This edition
constitutes a technical revision.
This edition includes the following significant technical changes with respect to the previous
edition:
a) the upper limit of the applicable frequency range has been extended from 110 GHz to
170 GHz;
b) circular disk resonators used for the measurements now include one with waveguide
interfaces;
– 4 – IEC 63185:2025 © IEC 2025
c) in calculating the complex permittivity from the measured resonant properties, the fringing
fields are now accurately taken into account based on the mode-matching analysis.
The text of this International Standard is based on the following documents:
Draft Report on voting
46F/699/FDIS 46F/702/RVD
Full information on the voting for its approval can be found in the report on voting indicated in
the above table.
The language used for the development of this International Standard is English.
This document was drafted in accordance with ISO/IEC Directives, Part 2, and developed in
accordance with ISO/IEC Directives, Part 1 and ISO/IEC Directives, IEC Supplement, available
at www.iec.ch/members_experts/refdocs. The main document types developed by IEC are
described in greater detail at www.iec.ch/publications.
The committee has decided that the contents of this document will remain unchanged until the
stability date indicated on the IEC website under webstore.iec.ch in the data related to the
specific document. At this date, the document will be
• reconfirmed,
• withdrawn, or
• revised.
MEASUREMENT OF THE COMPLEX PERMITTIVITY
FOR LOW-LOSS DIELECTRIC SUBSTRATES
BALANCED-TYPE CIRCULAR DISK RESONATOR METHOD

1 Scope
This document relates to a measurement method for complex permittivity of dielectric substrates
at microwave and millimeter-wave frequencies. This method has been developed to evaluate
the dielectric properties of low-loss materials used in microwave and millimeter-wave circuits
and devices. It uses higher-order modes of a balanced-type circular disk resonator and provides
broadband measurements of dielectric substrates by using one resonator, where the effect of
excitation holes and that of fringing fields are taken into account accurately on the basis of the
mode-matching analysis.
In comparison with the conventional method described in IEC 62810 and IEC 61338-1-3, this
method has the following characteristics:
'
• the values of the relative permittivity ε and loss tangent tanδ normal to dielectric plate
r
samples can be measured accurately and non-destructively;
surements by using higher-order modes by one
• this method presents broadband mea
resonator;
• this method is applicable for the measurements under the following conditions:
– frequency: 10 GHz ≤ f ≤ 170 GHz;
'
– relative permittivity: 1 ≤ ε ≤ 10;
r
–4 –2
– loss tangent: 10 ≤ tan δ ≤ 10 .
2 Normative references
There are no normative references in this document.
3 Terms and definitions
No terms and definitions are listed in this document.
ISO and IEC maintain terminology databases for use in standardization at the following
addresses:
• IEC Electropedia: available at https://www.electropedia.org/
• ISO Online browsing platform: available at https://www.iso.org/obp
4 Measurement parameters
The measurement parameters are defined as follows:
' ''
(1)
ε ε−jε
rr r
=
– 6 – IEC 63185:2025 © IEC 2025
'' '
(2)
tanδε= /ε
rr
' ''
ε
where ε and ε are the real and imaginary parts of the complex relative permittivity .
r r r
5 Theory and calculation equations
A resonator structure used in this method is shown in Figure 1. A thin circular conductor disk
R t
with radius and thickness is sandwiched between a pair of dielectric plate samples to be
c
'
measured having the same thickness t and dielectric properties ε and tanδ . Dielectric
r
samples are sandwiched by two parallel conductor plates.
The resonator is excited and detected by coaxial lines through excitation holes having radius
a
and length M . Because only the TM modes have the electric field in the centre of the
0m0
resonator, only those modes are selectively excited in the resonator, where the electric field
components in the resonator are normal to the plate samples for those modes. The resonator
has coaxial connectors or waveguide interfaces at input/output ports. For the latter case, for
selectively exciting the TM modes, the excitation holes of the resonator are excited in the
0m0
coaxial TEM mode using a coaxial-waveguide conversion.
'
ε and tanδ normal to the dielectric plates are determined from the measured values of the
r
f Q
resonant frequencies and the unloaded Q-factor for the TM mode by solving the
0 u
0m0
following resonant condition derived from the mode-matching analysis, where the exciting holes
and the fringing fields at the conductor disk edge are accurately taken into account:
'
det H ε ,f ,t,t ,R,a,M = 0
(3)
( )
r 0 c
tanδ=1/Q−1/Q 1+WW/
( )( ) (4)
u c 12
where
H is the NN× matrix derived from the boundary conditions;
is the number of terms of the series expansions for the mode-matching analysis;
N
Q
is the Q-factor due to the conductor loss;
c
W W
and are the electric energies stored in the dielectric region and the excitation hole
1 2
region, respectively.
W W Q
and are calculated from the mode-matching analysis, and can be approximately by
1 2 c
0,5
(5)
Qt /δ t(πf μσ)
c s 00
where
δ is the skin depth of the conductor;
s
σ is the conductivity;
μ is the permeability of free space.
Figure 1 – Structure of a circular disk resonator
The maximum measurable frequency is limited by the following cutoff frequencies:
Coax
a) cutoff frequency of coaxial lines used to excite the resonator f ;
c
Hole
b) cutoff frequency of excitation holes f ;
c
Rad
c) cutoff frequency for radial radiation through dielectric samples f .
c
For the case of the resonator with waveguide interfaces, the measurement frequency is also
limited by the operating frequencies of waveguide and internal coaxial-waveguide conversion.
Hole
f is calculated as a cutoff frequency for TM mode of a circular waveguide with radius a
c 01
and is given by
Hole
fc= χ / 2πa (6)
c 01
==
– 8 – IEC 63185:2025 © IEC 2025
where
χ ≈ 2,4048
is the first root of J x = 0 ;
( )
01 0
J x is the Bessel function of order 0 of first kind;
( )
c
is the light velocity.
Rad
t
f is determined by the sample thickness t , conductor disk thickness , and relative
c
c
'
permittivity ε and is given by
r
0,5

Rad '
f c / 22tt+ ε
( ) (7)
( )
c cr

'
Figure 2 shows the relations between f and ε for TM modes for R = 7,5 mm, t = 0,06 mm,
0 r 0m0 c
a = 0,465 mm, M = 1,5 mm, and t = 0,2 mm. Multiple resonances appear from 5 GHz to
' Rad
170 GHz for 1≤≤ε 10 (8 modes to 15 modes). Radiation limit ( f ) is also shown in Figure 2.
r c
Key
m is mode number of resonances in measurement
t
R 7,5 mm 0,06 mm
c
a 0,465 mm M 1,5 mm
t 0,2 mm
Figure 2 – Relation between resonant frequency and relative permittivity
The conductivity σ is measured by the two dielectric resonator method [1] .
___________
Numbers in square brackets refer to the Bibliography.
=
'
Measurement uncertainties of ε and tanδ are evaluated by considering the uncertainty
r
propagations of the resonant frequency, Q-factor, dimensions of resonator and samples, and
conductivity of the resonator, and by estimating the effect of the error of the mode-matching
analysis [2], [3].
6 Measurement system
Figure 3 shows a schematic diagram of a vector network analyzer measurement system for a
transmission-type resonator. A scalar network analyzer can also be used for measuring
equipment, because resonant frequencies and Q-factors can be derived from the frequency
S
dependence of the amplitude of the transmission, . However, a vector network analyzer has
an advantage in the precision of the measurement. Furthermore, resonant frequencies and
Q-factors are more accurate and less susceptible when they are derived from complex values
S S
of measured data by using the circle fitting on the complex plane of [4].
21 21
Figure 3 – Schematic diagram of a vector network analyzer measurement system
The structure of the resonator used in the complex permittivity measurements is shown in
Figure 1. A pair of dielectric plate samples to be measured, a thin circular conductor disk, and
two parallel conductor plates constitute a balanced-type circular disk resonator. The resonator
is excited by coaxial lines through excitation holes and under-coupled equally to the input and
output ports.
The resonant frequency f and the loaded Q-factor Q are derived from the frequency
0 l
dependence of S that is measured by using a vector network analyzer [4]. The unloaded
Q-factor Q is given by
u
LA (dB)/20
QQ / 1−10
(8)
ul ( )
where LA (dB) is the insertion attenuation at f .
0 0
=
– 10 – IEC 63185:2025 © IEC 2025
7 Measurement procedure
7.1 General
The measurements are carried out according to the following procedure. Examples of
measurement results and associated uncertainties for the complex permittivity are presented in
Annex A.
7.2 Preparation of measurement apparatus
Set up the measurement equipment and apparatus as shown in Figure 3. The cavity resonator
and dielectric samples shall be kept in a clean and dry state, as high humidity degrades
unloaded Q-factors.
7.3 Adjustment of measurement conditions
Set up the measurement conditions of a vector network analyzer. The interval between discrete
frequency points shall preferably be less than one tenth of the half width of the resonant
waveform. Intermediate frequency band width (IFBW), i.e. a digital band pass filter condition in
a vector network analyzer, is determined such that the noise floor is at least 20 dB lower than
the peak values.
7.4 Calibration of a vector network analyzer
A vector network analyzer shall be calibrated by using calibration kits.
7.5 Measurement of complex permittivity of test sample
Configure a balanced-type circular disk resonator with the pair of test samples. Figure 4 shows
the frequency dependence of S . Resonant frequencies of TM to TM modes are
21 010 050
indicated by the downward arrows. Measure the resonant frequency and unloaded Q-factor of
each mode and calculate the complex permittivity at each resonant frequency of test samples
by using Formula (3) and Formula (4).
The alignment between the conductor disk and excitation holes is critical to measurement
results, but it is possible to find a misalignment by detecting resonances of unwanted modes
between adjacent TM modes. In the frequency response of S , resonant peaks for
0m0 21
unwanted modes shall be at least 15 dB lower than those for adjacent TM modes.
0m0
S
Figure 4 – Frequency response of of balanced-type circular disk resonator
7.6 Periodic checkup of metal in resonator
Since the conductivity of the conductor plates and circular disk degrades due to oxidation of
the metals and scratches on the surfaces, the quality of the metals of the resonator shall be
checked periodically. It can be checked by measuring the conductivity by using the two dielectric
resonator method [1]. Instead, it can be checked by measuring the same low-loss sample
periodically. By checking the reproducibility of the measurement results of loss tangent of the
specified verification sample, it is possible to find the surface characteristic change in the metals
of the resonator.
– 12 – IEC 63185:2025 © IEC 2025
Annex A
(informative)
Example of measurement results and associated
uncertainties for complex permittivity
The measurement results and associated uncertainties for the complex permittivity of cyclic
olefin polymer (COP) sheet sample are obtained as follows. Hereafter, measurement
uncertainty of each quantity is expressed by its expanded uncertainty with a coverage factor of
.
k= 2
a) The parameters such as , , a , and of the resonator and t of the COP sample used
R t M
c
in the measurements are shown in Table A.1. The resonator used in this measurement
example is excited by 0,8 mm coaxial lines.
Table A.1 – Parameters of the resonator and the sheet sample
a t
R M
t
c
(mm) (mm) (mm) (mm) (mm)
8,982 ± 0,005 0,06 ± 0,004 0,47 ± 0,02 1,5 ± 0,1 0,251 ± 0,003

b) The resonant frequency f and unloaded Q-factor Q of the TM to TM modes in the
0 u 010 0,15,0
cavity with the COP sample are measured and shown in Table A.2. Uncertainty evaluations
of the resonant frequency and Q-factor are performed by considering the uncertainty
S
propagation of the uncertainty of , measurement repeatability, and the effect of
frequency resolution determined by the interval between discrete frequency points.
Monte-Carlo calculations are performed to evaluate the uncertainties of these resonant
properties [7].
Table A.2 – The resonant frequencies and unloaded Q-factors
Mode
f Q
0 u
(GHz)
TM 13,171 ± 0,007 385 ± 23
TM
24,178 ± 0,013 477 ± 24
TM 35,138 ± 0,017 539 ± 26
TM 46,101 ± 0,017 593 ± 25
TM 57,076 ± 0,012 645 ± 37
TM 68,057 ± 0,012 674 ± 24
TM 79,037 ± 0,017 713 ± 69
TM 90,010 ± 0,045 733 ± 68
TM
100,969 ± 0,079 756 ± 70
TM 111,878 ± 0,029 735 ± 74
0,10,0
TM 122,809 ± 0,030 792 ± 63
0,11,0
TM 133,677 ± 0,030 774 ± 59
0,12,0
TM
144,498 ± 0,035 814 ± 65
0,13,0
TM 155,210 ± 0,026 800 ± 61
0,14,0
TM 165,811 ± 0,036 782 ± 57
0,15,0
c) The conductivity of the metal of the resonator is measured by the two dielectric resonator
method at 10 GHz, and the result is σ= 5,63±×0,18 10 S/m.
( )
d) The measurement results of the complex permittivity of the COP sample are calculated by
deriving Formula (3) and Formula (4). Associated uncertainties are evaluated by considering
the uncertainty propagations of f , Q , t , R , t , a , M and σ . The effect of the finiteness
0 u c
of the number of terms used in the mode-matching analysis (relative convergence error) is
also considered in the uncertainty evaluation of the complex permittivity. The results are
shown in Table A.3.
Table A.3 – Measurement results of complex permittivity
Mode
'
−4
ε
tanδ 10
r
( )
TM 2,327 ± 0,005 2,73 ± 1,74
TM 2,326 ± 0,006 3,80 ± 1,21
TM 2,326 ± 0,007 4,35 ± 1,03
TM 2,326 ± 0,007 4,47 ± 0,82
TM 2,326 ± 0,008 4,35 ± 0,97
TM 2,326 ± 0,009 4,65 ± 0,64
TM 2,326 ± 0,009 4,56 ± 1,41
TM 2,327 ± 0,010 4,79 ± 1,32
TM 2,327 ± 0,010 4,87 ± 1,27
TM 2,327 ± 0,010 5,69 ± 1,41
0,10,0
TM 2,326 ± 0,009 5,07 ± 1,06
0,11,0
TM 2,326 ± 0,009 5,70 ± 1,03
0,12,0
TM 2,326 ± 0,009 5,35 ± 1,03
0,13,0
TM 2,326 ± 0,008 5,82 ± 1,00
0,14,0
TM 2,326 ± 0,008 6,35 ± 0,97
0,15,0
– 14 – IEC 63185:2025 © IEC 2025
Bibliography
[1] KOBAYASHI, Y, and KATOH, M, "Microwave Measurement of Dielectric Properties of
Low-Loss Materials by the Dielectric Rod Resonator Method," IEEE Trans. Microw.
Theory Tech., vol. 33, no. 7, pp. 586-592, July 1985
[2] KATO, Y and HORIBE, M, "Permittivity measurements and associated uncertainties up
to 110 GHz in circular-disk resonator method," 2016 46th European Microwave
Conference (EuMC), London, 2016, pp. 1139-1142
[3] KATO, Y and HORIBE, M, "Broadband Permittivity Measurements up to 170-GHz Using
Balanced-Type Circular-Disk Resonator Excited by 0.8-mm Coaxial Line," IEEE Trans.
Instrum. Meas., vol. 68, no. 6, pp. 1796–1805, Jun 2019
[4] KATO, Y and HORIBE, M, "Comparison of calculation techniques for Q-factor
determination of resonant structures based on influence of VNA measurement
uncertainty," IEICE Trans. Electron., vol. E97-C, no. 6, pp. 575–582, Jun 2014
[5] KAWABATA, H HASUIKE, K.I., KOBAYASHI, Y and MA, Z, "Multi-Frequency
Measurements of Complex Permittivi
...